To some it may sound absurd, but at least one other scholar has recognized that Tolkien likely buried links within TLotR to that most famous English fairytale: Jack and the Beanstalk. That person being Mark Hooker (see The Hobbitonian Anthology) who has identified linkage to item (vii) below.

Ms. Seth has obviously investigated the matter in some detail and connected in Tom Bombadil too.

(i) The funny old man who handed magical beans to Jack was a fairy being, and in Tolkien's myth - modeled intentionally to be Tom.

(ii) In trade for Jack's very productive cow, Milky-White, the technical owner became Tom – who she deduces, per TLotR, has access to a cow. A strong hint dropped by Tolkien (apart from all the dairy produce present) is the 'white' river of 'milk' emanating from his residence.

(iii) Both heroes (Frodo & Jack) awake in the morning to stare out of a window at beanstalks.

(iv) The Black Riders are ogrish in size compared to the hobbits and similarly chase the hobbits as the ogre did in the Jack tale.

(v) The smelling of blood and the hatred displayed by the Black Riders echoes the Fe-fi-fo-fum rhyme of Jack and the Beanstalk.

(vi) A horn is blown in both TLotR and Jack and the Beanstalk to rally the people against the 'ogre' foes.

(vii) The famous Fe-fi-fo-fum rhyme was intentionally included in TLotR but slightly distorted to reflect oral diffusion down in to our world's mythology.

The writer promises additional evidence that have been missed by practically all readers/scholars in a future essay.

(viii) The miller and the farmer from Sarehole – being named as Ogres by the Tolkien boys – and the miller being covered in bone-dust.
(ix) Farmer Magott having etymological links to 'Goemagot' – a British Giant – pointed out by M. Hooker
(x) Farmer Maggot being cast with an ogre-like personality in an early draft per M. Hooker.
(xi) The name Bamfurlong – having etymological linkage to a long field of beanstalks – perhaps with the intention of representing one tangled-up giant one.

Eleven is kind of getting up there for the whole affair being pure coincidence. Still – as in all these matters – when it's not clearly spelled out by Tolkien – it's always conjectural. In this case though, I hark back to one of Tolkien's comments per Letter #180:

"Having set myself a task, ... being precisely to restore to the English an epic tradition and present them with a mythology of their own ...”.

I have to wonder which “epic tradition” and what exactly did he want to “restore”? Did he mean Arthurian myth – which are not entirely native English stories?

I'm not so sure why the tale of the Beanstalk and 'Jack' – as Ms. Seth states being “a quintessential part of traditional English folklore” - would have been excluded from LotR, especially as so much other myth/folklore from our world wasn't!